Let X be a Banach space with norm ∥ ⋅ ∥ . Let A : D (A) ⊂ X → X be an (possibly unbounded) operator that generates a uniformly bounded holomorphic semigroup. Suppose that ε > 0 and T > 0 are two given constants. The backward parabolic equation of finding a function u : [ 0 , T ] → X satisfying u t + A u = 0 , 0 < t < T , ∥ u (T) - φ ∥ ⩽ ε , for φ in X, is regularized by the generalized Sobolev equation u α t + A α u α = 0 , 0 < t < T , u α (T) = φ , where 0 < α < 1 and A α = A (I + α A b ) - 1 with b ⩾ 1 . Error estimates of the method with respect to the noise level are proved. [ABSTRACT FROM AUTHOR]